Random sampling of non-overlapping substrings of length k

Given a string of length n, how would I (pseudo)randomly sample m substrings of size k such that none of the sampled substrings overlap? Most of my scripting experience is in Perl, but an easy-to-run solution in any common language will suffice.

If there is a character that cannot occur in the input, e.g. X, just:

my $size = 20;
my $count = 20;
my $mark = 'X';
my $input = 'CCACGCATTTTTGTTCATTGTTCTGGCTTCTTACAAGGTTCAGTAGACTTTGTAACACAGTTGTGTCTCTCACAGATTGGCAGATGTTTGGTAAAGGATTGACTTTTCAGCCAACTCATGGGAAAGTGAAATAATGTAAAAAACAGGAAGAATACAGTTTTAGGCCTTTCAAGTGAGGCATGGCTTTCAGCTCTTGGCAAGAACAGGCAAGGAGATGCAAGTTTTAGGACTCTAAGAGGCTAGGCTTTTCAAAGTGCTTCTCTCCCCTTCACCCTCCTTCAGTTACAGCACCAAGCACCACCGAGGTGTTACCTGCAGCCTCACTCTCTACCTGGTTGTGGGATCCTGCCACTTCCTTAACCCACACTGAGTTCCTTGTGGTTCACAGGGTCACACAGAGGGCTGTAGAGATACAAAAGATATATGTGATTTTATATCACCTATCATATGAAGATATATTTATAAAATAGGAAACATATTAACCACTTATCATTTTATATATTTATGGTTTTATGTGTCAAAAATATATTGTTTCATGTATGTATTAAAGGATAAGTATGTATAAGAGGTTTTATAGATGTGTAAAATTATATATTTATACGTATCTTTACAAATTTAAGAATAAAGGAAGGAAAATTCTCAAAGAGGAATTCAGATATCAAGCAGTGCCCTTTGACCAAGAGCCTTGGTTACAACATACCTACAAAAGTGAACTATCATTGAAAGACCTATGGACACTGGATTTCTCTTTCCTTATTTAGAAGGGCAGTCTGTGTCTTGGAAAAGCATACAGTTTGTTGTATCTTGCTGGACAACAGGAGTCA';

if (2*$size*$count-$size-$count >= length($input)) {
    die "selection may not complete; choose a shorter length or fewer substrings, or provide a longer input string\n";
}

my @substrings;
while (@substrings < $count) {
    my $pos = int rand(length($input)-$size+1);
    push @substrings, substr($input, $pos, $size, $mark x $size)
        if substr($input, $pos, $size) !~ /\Q$mark/;
}